Interferometric servo control system for stage metrology

ABSTRACT

The invention features a method for determining non-linear cyclic errors in a metrology system that positions a measurement object under servo-control based on an interferometrically derived position signal. The method includes: translating the measurement object under servo-control at a fixed speed; identifying frequencies of any oscillations in the position of measurement object as it is translated at the fixed speed; and determining amplitude and phase coefficients for sinusoidal components at the identified frequencies which when combined with the position signal suppress the oscillations. The invention also features a method for positioning a measurement object under servo-control based on an interferometrically derived position signal indicative of a position for the measurement object. This method includes: generating a compensated position signal based on the interferometrically derived position signal and at least one correction term that has a sinusoidal dependence on the position of the measurement object; and repositioning the measurement object based on the compensated position signal and a desired position for the measurement object.

CROSS-REFERENCE TO RELATED APPLICATIONS

Pursuant to 35 U.S.C. §120, this application is a continuation andclaims the benefit of prior U.S. application Ser. No. 10/819,257, filedApr. 5, 2004 now U.S. Pat. No. 6,956,656, which is a continuation ofprior U.S. application Ser. No. 09/879,428, filed Jun. 12, 2001 now U.S.Pat. No. 6,747,744, which claims priority under 35 U.S.C. § 119(e) toprovisional patent application no. 60/252,108, filed Nov. 20, 2000. Thecontents of the prior applications are incorporated herein by reference.

BACKGROUND

Microlithography and electron beam writing are examples of applicationsthat generate precise patterns on a sample, such as a semiconductorwafer or mask. Such applications require accurate placement and/ormovement of the sample stage relative to the writing tool. Often,accurate positioning of different components within the writing tool,such as the relative position of a reticle in a lithography tool, alsorequires accurate positioning.

To enable such accurate positioning, heterodyne distance measuringinterferometers are often used to measure distance changes along one ormore axes. The distance measurements can provide a control signal thatdrives a servo system for accurately positioning different components ofa given system.

A heterodyne distance measuring interferometer measures changes in theposition of a measurement object relative to a reference object based onoptical interference generated by overlapping and interfering ameasurement beam reflected from a measurement object with a referencebeam. Measurement of the optical interference produces an interferenceintensity signal that oscillates at a heterodyne angular frequency ωcorresponding to small difference in frequency between the measurementand reference beams. Changes in the relative position of the measurementobject correspond to changes in the phase φ of the oscillating intensitysignal, with a 2π phase change substantially equal to a distance changeL of λ/(np), where L is a round-trip distance change, e.g., the changein distance to and from a stage that includes the measurement object, λis the wavelength of the measurement and reference beams, n is therefractive index of the medium through which the light beams travel,e.g., air or vacuum, and p is the number of passes to the reference andmeasurement objects.

Unfortunately, this equality is not always exact. Many interferometersinclude nonlinearities such as what are known as “cyclic errors.” Somecyclic errors can be expressed as contributions to the phase and/or theintensity of the measured interference signal and have a sinusoidaldependence on the change in optical path length pnL. In particular, thefirst harmonic cyclic error in phase has a sinusoidal dependence on(2πpnL)/λ and the second harmonic cyclic error in phase has a sinusoidaldependence on 2(2πpnL)λ. Higher order and sub-harmonic cyclic errors canalso be present.

SUMMARY

The invention relates to metrology systems in which an interferometricmeasurement provides a control signal for a servo system that positionsa device, such as a lithographic stage. The applicant has recognizedthat, in the absence of any cyclic error compensation, cyclic errors inthe interferometric measurement are a source of a false error signal inthe servo system and can cause deviations in the desired position of thedevice, e.g., stage oscillations. In particular, depending on propertiesof the complex open-loop gain of the servo system as a function offrequency, the deviations can comprise oscillations with amplitudes thatare either as large as the magnitude of the cyclic error(s) in theinterferometric measurement or significantly exceed the magnitude of thecyclic error(s). Such deviations, however, provide an observable foridentifying and quantifying such cyclic errors. The quantified cyclicerrors can be used to generate a compensation signal that corrects theinterferometric control signal and thereby eliminating the source of thefalse error signal in the servo system and improves the accuracy of thestage metrology system.

In general, in one aspect, the invention features a method fordetermining nonlinear cyclic errors in a metrology system that positionsa measurement object (e.g., a stage in a lithography or beam writingtool) tinder servo-control based on an interferometrically derivedposition signal. The method includes: translating the measurement objectunder servo-control at a fixed speed; identifying frequencies of anyoscillations in the position of measurement object as it is translatedat the fixed speed; and determining amplitude and phase coefficients fora sinusoidal correction term at one of the identified frequencies whichwhen combined with the position signal suppress the oscillations at thatfrequency.

Embodiments of the method may further include any of the followingfeatures.

The method may further include the steps of repeating the translating,identifying, and determining steps for each of multiple, additionalfixed speeds; and generating a representation of the nonlinear cyclicerrors based on the coefficients and identified frequenciescorresponding to the oscillations at each of the fixed speeds.

In some embodiments, the interferometrically derived position signal isthe phase of an interferometric intensity signal at a heterodynefrequency. In other embodiments, the interferometrically derivedposition signal is a heterodyne, interferometric intensity signal.

To combine the sinusoidal correction signal with the position signal,the sinusoidal correction term man be, for example, subtracted from oradded to the position signal to suppress the oscillations.

In general, in another aspect, the invention features a method forpositioning a measurement object (e.g., a stage in a lithography or beamwriting tool) under servo-control based on an interferometricallyderived position signal indicative of a position for the measurementobject. The method includes: generating a compensated position signalbased on the interferometrically derived position signal and at leastone correction term that has a sinusoidal dependence on the position ofthe measurement object, and repositioning the measurement object basedon the compensated position signal and a desired position for themeasurement object.

Embodiments of the method may include any of the following features.

For example, the veneration of the compensated position signal mayinclude; determining a speed for the measurement object based on theinterferometrically derived position signal, and selecting parametersfor the at least one sinusoidal correction term based on the determinedspeed.

The compensated position signal may be generated by subtracting the atleast one sinusoidal correction term from the interferometricallyderived position signal.

The interferometrically derived position signal may be the phase of aninterferometric intensity signal at a heterodyne frequency.Alternatively, the interferometrically derived position signal may be aheterodyne, interferometric intensity signal.

The at least one sinusoidal correction term ma include multiplesinusoidal correction terms (e.g., two, three, or more such terms). Eachof the multiple sinusoidal correction terms may correspond to a cyclicerror in the interferometrically derived position signal.

In general, in another aspect, the invention features an electronicprocessing system for use with a servo-system for positioning ameasurement object. The electronic processing system includes: an inputport configured to receive a position signal from an interferometrysystem indicative of a position for the measurement object; a memorystoring a representation of nonlinear errors in the interferometrysystem; a processor which during operation generates a compensatedposition signal based on the position signal from the interferometrysystem and the stored representation; and an output port configured todirect the compensated position signal to a servo-controller.

Embodiments of the electronic processor may include any of the followingfeatures.

For example, the stored representation of nonlinear errors may beexpressed as a sum of multiple correction terms each having a sinusoidaldependence on the position of the measurement object.

The stored representation of nonlinear errors may be parameterized by aspeed of the measurement object. For example, during operation theprocessor may further determine an estimate for the speed of themeasurement object based on the position signal from the interferometrysystem, and generate the compensated position signal based on theposition signal from the interferometry system, the storedrepresentation of nonlinear errors, and the estimated speed.

Other features, objects, and advantages of the invention will beapparent from the description and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a servo-controlled stage metrologysystem.

DETAILED DESCRIPTION

The invention features a method for identifying, and quantifying cyclicerrors in a servo-controlled interferometric metrology system. Oncequantified, cyclic errors in the interferometric control signal can beremoved to suppress errors that may otherwise cause oscillations in themetrology system because of positive feedback.

Interferometry systems that quantify and compensate for non-linearities,such as a cyclic errors, and the application of such interferometrysystems to microlithography and beam writing applications are disclosedin the following U.S. patent and U.S. patent applications, the contentsof which are incorporated herein by reference: U.S. Pat. No. 6,137,574to Henry Allen Hill entitled “Systems and Methods for Characterizing andCorrecting Cyclic Errors in Distance Measuring and DispersionInterferometry;” U.S. patent application Ser. No. 09/557,338 filed Apr.24, 2000, by Henry Allen Hill entitled “Systems and Methods forQuantifying Nonlinearities in Interferometry Systems;” and U.S. patentapplication Ser. No. 09/583,368 filed May 30, 2000, by Henry Allen Hillentitled “Systems and Methods for Quantifying Nonlinearities inInterferometry Systems.”

FIG. 1 is a schematic diagram of a stage metrology system 100, whichincludes a translatable stage 60 for supporting, e.g., a wafer orreticle in a microlithography tool, a translator 62 for translatingstage 60 along an axis, and an interferometer 30 for measuring thetranslations along the axis.

During operation, source 10 generates an input beam 12 including twocoextensive orthogonally polarized components that are frequency-shiftedone with respect to the other. In the presently described embodiment,source 10 includes a coherent source of a single frequency optical beamsuch as a laser and an acousto-optical modulator to generate the twofrequency-shifted components of beam 12. In other embodiments, source 10can be, for example, a laser source that venerates the frequency-shiftedcomponents intracavity, such as in a Zeeman-split laser. Input beam 12is incident on interferometer 30. One frequency component of beam 12defines a measurement beam 14 that contacts a mirror 50 connected tostage 60 and is subsequently; reflected back to interferometer 130. Theother frequency component defines a reference beam, which interferometer30 combines with the reflected measurement beam to form an output beam16. Interferometer 30 can be any of a number of interferometers, forexample, it can be a single-pass dynamic interferometer (see, e.g., PCTapplication US99/19904 filed Aug. 31, 1999), a double-pass highstability plane mirror interferometer, a double-pass differential planemirror interferometer, or some other angle or linear displacementinterferometer such as those described in the article entitled“Differential interferometer arrangements for distance and anglemeasurements: Principles, advantages and applications” by C. Zanoni, VDIBerichte Nr. 749, 93–106 (1989).

Referring again to FIG. 1, mirror 32 reflects output beam 16 to detector32, which measures the intensity of the output beam using, for example,a quantum photon process, to produce an electronic interference signal,heterodyne signal 20. The phase of heterodyne signal 20 is related tothe linear displacement of stage 60. In particular, in the absence ofany non-linearities such cyclic errors, signal 20 can be expressed ass(t) wheres(t)=a cos(ωt+φ+ζ),   (1)φ=Lkn,   (2)where L is the linear displacement given by the physical path lengthdifference between the reference and measurement paths, k is the wallnumber of tale measurement beam, n is the refractive index within theinterferometer, ω is the angular difference frequency between themeasurement and reference beams, t is time, α is an amplitude that isconstant with respect to φ, and ζ is a phase offset that is constantwith respect to φ and {dot over (φ)}, where {dot over (φ)} is the firstderivative of φ with respect to time. In the subsequent treatment, weset ζ=0. Detector 32 transmits signal 20 in, e.g., a digital format, toelectronic processor 34, which determines the phase φ of signal 20 by aphase detector using, for example, a fast Fourier transform of signal20.

In the presence of non-linearities, however, such as those described inthe U.S. patents and patent applications incorporated by referenceabove, the phase determined by electronic processor 34 is φ′=φ+ψ, whereis ψ corresponds to a contribution from non-linearities, which cangenerally be expressed as:

$\begin{matrix}{\psi = {\sum\limits_{n}{A_{n}{\cos\left( {\omega_{n}^{t} + {p_{n}\varphi} + \zeta_{n}} \right)}}}} & (3)\end{matrix}$where A_(n), ζ_(n), ω_(n), and p_(n) are the amplitude, phase offset,frequency, and harmonic index, respectively, of the nth nonlinear term.The harmonic index p_(n) can take on integer and fractional values.Also, for many nonlinear terms, the frequency ω_(n) is zero. Forexample, the first harmonic cyclic error corresponds to a value of onefor p_(n) and a value of zero for ω_(n). As described in the U.S.patents and patent applications incorporated herein by reference above,other types of cyclic errors, such as non-linearity in detector 32 andaliasing effects, can produce additional values for p_(n) such assub-harmonic values and frequencies dependent upon the samplingfrequency of an analog-to-digital converter used in conversion of s(t)to a digital format. Furthermore, the amplitude and phase of eachnonlinear term often varies with the speed of the stage, which isrelated to the instantaneous rate of change of phase φ, denoted as {dotover (φ)}.

Electronic processor 34 sends a signal 22 indicative of the determinedphase φ′ to both electronic processors 36 and 38. Electronic processor36 stores a quantified representation of at least one or some of thenon-linearities generally present in the interference signal because ofimperfections in interferometer 30. For example, electronic processor 36can store values of the nonlinear coefficients A_(n), ζ_(n), ω_(n), andp_(n) for at least one or some of the nonlinear terms, which permit itto estimate the value of ψ from the value of φ′ in signal 22. Suchdetermination can, for example, involve an iterative calculation of ψbased on the initial assumption that φ≈φ′.

Where necessary, electronic processor 36 also stores the stage speeddependence of the quantified non-linearities. For example, the amplitudeand phase estimates stored by electronic processor 36 for the nonlinearcoefficients can be parameterized with respect to {dot over (φ)}, inother words, the stored estimates can be indicative of A_(n) ({dot over(φ)}) and ζ_(n) ({dot over (φ)}). In such embodiments, electronicprocessor 34 determines values for the phase φ, and its instantaneousrate of change {dot over (φ)}, and sends both values to electronicprocessor 36 as signal 22. Electronic processor 36 then approximates{dot over (φ)}≈{dot over (φ)}′ to determine the stage speed dependenceof A_(n) ({dot over (φ)}) and ζ_(n)({dot over (φ)}), or alternatively,determines {dot over (φ)} from {dot over (φ)}′ in an iterative process.In other embodiments, electronic processor 36 can receive an additionalinput from all independent source that monitors the stage speed. In anycase, electronic processor 36 uses its stored, quantified representationto determine the nonlinear contribution ψ to the phase φ′ determined byelectronic processor 34.

Electronic processor 36 sends the determined value for ψ to electronicprocessor 38 as compensation signal 24. Electronic process 38 then usescompensation signal 24 to remove the estimated nonlinear contributionsfrom the measured phase φ′ and generate a compensated signal 26indicative of the phase φ, which is directly related to the stagedisplacement through Equation 2. Electronic processor 36 sends thecompensation signal 26 to servo controller 52, which compares the staredisplacement indicated by signal 26 to the desired stage displacementcorresponding to an input control signal 29 to generate a servo signal28. Servo controller then sends servo signal 28 to translator 62 tocorrect any deviation of the translation of the stage 60 from a desiredtranslation time course. Generally, translator 62 may also receive anadditional signal (not shown) similar to input control signal 29 (whichprovides the desired stage translation time course) for coarselytranslating stage 60, with the interferometrically driven servo-systemproviding fine translation adjustment.

In other embodiments, the representation of the quantifiednon-linearities in electronic processor 36 can be with respect theintensity of the interference signal rather than its phase at theheterodyne angular difference frequency ω. In such embodiments, theinterferometric intensity signal measured by the detector may beexpressed as:s′(t)=s(t)+s _(NL)(t)   (4)where s′(t) is the measured intensity, s(t) is the intensity that wouldbe measured in the absence of any non-linearities, and s_(NL)(t) is thenonlinear contribution to the measured intensity. The non-linearitiesare then expressed as a sum of sinusoidal contributions, e.g.,

$\begin{matrix}{{s_{NL}(t)} = {\sum\limits_{q}{B_{q}\left\{ {\sum\limits_{u \cdot p}{a_{up}{\cos\left( {{u\;\omega\; t} + {p\;\varphi} + \zeta_{up}} \right)}}} \right\}^{q}}}} & (5)\end{matrix}$where p=1, 2, 3 . . . , and fractional values, u=0 or 1, and q=1, 2, 3 .. . , and where the “q” index is associated with non-linearity indetector 32. Thus, in such embodiments, electronic processor 36 can, forexample, store the amplitude and phase coefficients for at least one orsome of the nonlinear terms in Equation (5) and, where appropriate,their stage speed dependence.

Furthermore, in such embodiments; electronic processor 34 can determineφ′ from s′(t) and send s′(t), φ′, and {dot over (φ)}′ to electronicprocessor 36 and s′(t) to electronic processor 38 as signal 22.Electronic processor 36 then determines an estimate for s_(NL)(t) basedon the stored, quantified non-linearities and sends that estimate toelectronic processor 38 as signal 24. In turn, electronic processor 38removes the nonlinear contribution s_(NL) (t) from the measuredintensity the measured intensity s′(t) to provide a compensated estimatefor s(t), determines the phase φ, which is directly related to the stagedisplacement through Equation 2, and generates compensated signal 26indicative of the phase. Electronic processor 38 sends the compensationsignal 26 to servo controller 52, as in the first embodiment.

In any of these embodiments, the quantified representation ofnon-linearities stored by electronic processor 36 can be determined byany of the methods described in the U.S. patents and applicationsincorporated herein by reference above. They can also be determinedthrough another method described below.

Applicant has recognized that non-linear contributions in signal 26 sentto servo controller 52 can produce a false error signal in the servosystem that cause stage oscillations that may be as large as or greatlyexceed the amplitude of the non-linear errors in the interferometricallymeasured displacement.

Consider, for example, a stage translation speed of 25 micron/sec and adouble pass interferometer used to measure the corresponding translationand provide the error signal to the servo controller. For this example,the first harmonic cyclic error will have a frequency of 158.0 Hz for aHelium Neon source laser operating at 633 nm and the one-halfsub-harmonic cyclic error will have a corresponding frequency of 79.0Hz. Both of these frequencies are typically within the bandwidth of theservo system, and can therefore lead to stage oscillations at thesefrequencies. The cyclic error amplitude required to produce anunacceptable level of stage oscillation will depend on the complexopen-loop gain of the servo system. However, cyclic error amplitudes ofthe order of nanometers may generate an unacceptable level of stageoscillation. Frequencies of cyclic errors that lead to substantiallypositive feedback in the servo system generate the largest amplitudes instage oscillation. Such stage translations of the order of 25 micron/secalong an axis can arise during, for example, an alignment procedure.They can also occur during a high-speed translation along a second axiswherein the stage mirror for the first axis is not orthogonal to thetranslation axis associated with the second axis by an angle of theorder of 100 microradians.

Nonetheless, observation of such state oscillations provides a method ofidentifying and quantifying those cyclic errors that produce the stageoscillations.

First, one translates the stage at a fixed speed under closed loop servocontrol. For example, the stage metrology system 100 is operated withinput control signal 29 set for a constant translation speed. Iffeedback of one or more non-linearities in interferometric signal 20occurs at that speed, stage oscillations result and correspond to anoscillatory deviation of stage 60 from desired speed at one or morecorresponding frequencies. One can measure such deviations from thephase φ′ determined by electronic processor 34 because the non-linearerror in φ′ serving as a false error source will typically be of theorder of the stage oscillation amplitude or small compared to the stageoscillation amplitude. Alternatively, one can independently measure thestage oscillations using, e.g., a mechanical or machine visionmeasurement.

One can then determine the frequency components of oscillatorydeviations by Fourier analysis. The resulting frequencies equal theω_(n)+p_(n){dot over (φ)} frequencies in Equation (3). For each of thesefrequencies, electronic processor 36 determines ω_(n) and p_(n) byassuming that {dot over (φ)}≈{dot over (φ)}′. Then, for each frequency,electronic processor 36 iteratively determines amplitude A_(n) and phaseoffset ζ_(n), coefficients for a correction term. A_(n)cos(ω_(n)t+p_(n)φ′+ζ_(n)), which, when subtracted from the measuredphase φ′ in electronic processor 38, provides a compensated signal 26 toservo controller 52 that suppresses the stage oscillations it thatfrequency. Alternatively, the electronic processor can determine thecoefficients by adding the correction term to the measured phase, inwhich case the phase offset ζ_(n) coefficient will shift by π radians.

Once all of the stage oscillation frequencies have been suppressed theprocess is repeated at additional fixed speeds for the stage todetermine the frequencies and corresponding amplitude and phasecoefficients at each new speed. The resulting frequencies andcoefficients are stored in electronic processor 36 to definite, or addto, the stored quantified nonlinear representation used during normaloperation.

The quantification method can be applied similarly to embodiments wherethe non-linearities are expressed as sinusoidal contributions to theintensity measured by detector 32, s′(t).

Other aspects, advantages, and modifications are within the scope of thefollowing claims.

1. A method comprising: a) positioning a stage relative to energy usedto expose a sample supported by the stage; b) measuring values of adistance measuring interferometry signal indicative of the relativeposition of the stage for a first period of time; c) using the valuesfrom the first period of time to determine one or more correctionfactors for the distance measuring interferometry signal, wherein thecorrection factors relate to cyclic errors in a distance measuringinterferometer used to produce the distance measuring interferometrysignal; d) measuring at least one value of the distance measuringinterferometry signal during a second period of time following the firstperiod of time; e) correcting the value from the second period of timebased on the correction factors; and f) using the corrected values fromthe second period of time to improve the relative positioning of thestage.
 2. The method of claim 1, wherein the one or more correctionfactors comprises multiple correction factors.
 3. The method of claim 1,wherein the at least one value from the second period of time comprisemultiple values.
 4. The method of claim 1, wherein the at least onevalue from the second period of time comprise multiple values.
 5. Themethod of claim 1, wherein the stage is a microlithography stage.
 6. Themethod of claim 1, wherein the sample is a wafer or a reticle.
 7. Themethod of claim 1, wherein the energy is radiation.
 8. The method ofclaim 1, wherein the energy is an electron beam.
 9. The method of claim1, further comprising estimating a relative speed of the stage based onthe measured values from the first period of time, and correcting thevalue from the second period of time based on the correction factors andthe estimated speed.
 10. The method of claim 1, wherein the values ofthe distance measuring interferometry signal are phase values at aheterodyne frequency of a heterodyne interferometry signal.
 11. Themethod of claim 1, wherein the values of the distance measuringinterferometry signal are intensity values of a heterodyneinterferometry signal.
 12. The method of claim 1, wherein the correctionfactors have a sinusoidal dependence on the relative position of thestage.
 13. Apparatus comprising: an exposure system configured to directenergy to a sample; a stage system configured to support the sample andposition the sample relative to the energy from the exposure system; adistance measuring interferometer coupled to the stage system andconfigured to produce a distance measuring interferometry signalindicative of the relative position of the stage; and an electronicprocessor coupled to the stage system and the distance measuringinterferometer, wherein the electronic processor is configured to: i)determine one or more correction factors for the distance measuringinterferometry signal based on values from the distance measuringinterferometry signal for a first period of time, wherein the correctionfactors relate to cyclic errors in a distance measuring interferometerused to produce the distance measuring interferometry signal; ii)correct one or more values from the distance measuring interferometrysignal for a second period of time based on the correction factors; andiii) use the corrected values from the second period of time to causethe stage system to improve the relative positioning of the sample. 14.The apparatus of claim 13, wherein the exposure system is amicrolithography exposure tool.
 15. The apparatus of claim 13, whereinthe exposure system is a beam writing tool.
 16. The apparatus of claim13, wherein the one or more correction factors comprises multiplecorrection factors.
 17. The apparatus of claim 13, wherein the one ormore values from the second period of time comprise multiple values. 18.The apparatus of claim 16, wherein the one or more values from thesecond period of time comprise multiple values.
 19. The apparatus ofclaim 13, wherein the sample is a wafer or a reticle.
 20. The apparatusof claim 13, wherein the electronic processor is further configured toestimate a relative speed of the sample based on the measured valuesfrom the first period of time, and correct the values from the secondperiod of time based on the correction factors and the estimated speed.21. The apparatus of claim 13, wherein the values of the distancemeasuring interferometry signal are phase values at a heterodynefrequency of a heterodyne interferometry signal.
 22. The apparatus ofclaim 13, wherein the values of the distance measuring interferometrysignal are intensity values of a heterodyne interferometry signal. 23.The apparatus of claim 13, wherein the correction factors have asinusoidal dependence on the relative position of the stage.
 24. Amethod for fabricating integrated circuits comprising using the methodof claim 1, wherein the sample comprises a wafer on which the integratedcircuit is fabricated or a reticle through which the wafer is exposed.25. A method for fabricating integrated circuits comprising using theapparatus of claim 13, wherein the sample comprises a wafer on which theintegrated circuit is fabricated or a reticle through which the wafer isexposed.